1. Field of the Invention
This invention relates to a servo system for controlling the position of a read/write head over a rotating data disk. More particularly, it relates to the addition of a compensation scheme to the feedback loop of the servo that causes the gain of the servo to increase only in a very narrow spectrum of its operating bandwidth. In a preferred embodiment, the compensation takes the form of a second order digital filter combined with a proportional-integral-differential phase compensation filter in the feedback loop of an embedded servo system for a digital data disk drive.
2. Background
One of the most important data storage devices for digital computers is a class of devices known as disk drives. A disk drive consists of a rotating disk with magnetic media deposited on one or more surfaces in concentric information tracks. Information is stored in the magnetic media by causing magnetic domains to be in one of two polarities. The domains are switched from one polarity to another, in a write operation by a transducer. The same transducer also detects the state of each domain. The transducer and its mechanical housing is referred to as a "head".
Information is communicated to and from the disk by placing the head over a desired track and performing either a read or a write operation. The head is positioned by a mechanical arm called an actuator. The actuator is in turn caused to move by an electric motor which is connected through a digital to analog converter and amplifier to a digital computer. Here the term digital computer is used to mean any digital device utilizing logic and memory such as a microprocessor in conjunction with proms.
In the fabrication of disk drives, a hole is drilled as close to the center of the disk as the manufacturing process allows, and the disk is clamped to the shaft of an electric motor. The motor turns the disk. In this process, every effort is made to drill the hole and place the shaft around which the disk rotates in the precise center of the disk. But because of the tolerances in any manufacturing process, the hole is never exactly in the center of the disk.
Having the hole in the center of the disk is important when it comes to positioning the head over the disk. Because the information is written on tracks, the head must remain over the relevant track as the disk spins underneath the head. If the tracks are perfectly concentric, once the head is positioned over the proper track, the head never has to move. But if the tracks are not perfectly concentric, the track will move radially relative to the head, and the head will be forced to move if it is to keep the track directly beneath it.
One of the techniques developed to minimize this problem consists of writing the tracks after the center hole has been drilled and the shaft inserted and clamped. With precise track writing equipment the track may be written in a distorted manner that exactly compensates for the hole being not in the center of the disk. Thus, when the disk spins, the track will move beneath the head as if it were perfectly concentric with the shaft.
This technique works well under most circumstances. But, if the disk slips on the shaft after track writing, it will cause all of the tracks to oscillate in inertial space. And the frequency of the oscillation will be at the angular speed at which the disk spins. Typically this is between 60 and 80 revolutions per second. Thus, a track will not slide by directly under the head, but will appear to move radially.
Disks slip on their shaft when they are dropped or otherwise experience a mechanical shock. For desk top and larger computers, this is rare. For portable computers, it is not rare. And with the current state of the art, simply further tightening the clamp is not the answer since clamping tight enough to prevent slippage can cause the disk to warp.
As a first step in solving this problem, all disk manufacturers, use a servo loop to cause the head to "track" the data track. The servo loop controls the acceleration of the head caused by an electric motor that drives the actuator. The input to the servo are measurements of head position made by the head itself. The head position is determined from position indicators written directly onto the disk. That is, a certain number of bits of information on each track are reserved for providing position information. As the head passes over the indicators, the track over which the head is sitting is detected by the head itself and supplied to the servo. The indicators are at regularly spaced locations. Thus the input to the servo is not continuous, but is sampled.
In order for the servo to be effective, it must act quickly enough to cause the head to follow any radial movement of the track without losing data. Conventional servo design theory teaches that the ability of the servo loop to reject an external disturbance is a direct function of the open loop gain of the servo over the bandwidth of the disturbance. An external disturbance is anything that tends to cause a position error between the data track on the disk and the head. For definitional purposes, the bandwidth of the servo system may be conveniently defined as extending from a frequency of zero to the frequency at which the open loop gain is zero.
As with all servo systems that have other than all passive components, system stability is always a concern and a key design parameter. A servo may be said to be stable if, for small values of input, the output remains small or does not increase with time and thus without limit. A servo is known to be unstable if at the unity gain crossover point, that is the frequency at which the gain is one, the phase lag between the output and the input is 180 degrees.
This can be seen by reference to FIG. 1 which illustrates in block diagram form the most elemental servo system. In FIG. 1, a basic servo system consists of a plant/compensator element 10 and a feedback gain element 12 that takes the output back to the input. The modified output signal is then subtracted from the input signal at summing junction 14. The transfer function of this block diagram is set out in Equation 1 below: ##EQU1## where G is the gain and H is feedback gain. As can be seen, where the open loop gain, GH, equals -1, which is at zero decibels (db) of gain and a phase shift of -180 degrees, the denominator is zero and the expression becomes infinite, i.e. servo instability. Thus, merely closing a loop around an active element such as a transistor or a motor (referred to as the "plant" or the "dynamic equipment") can lead to an unstable servo. This problem is addressed by inserting compensation elements in the forward path of the loop. The main purpose of the compensation is to "peak the phase at the zero db crossover point". That is, the purpose is to modify the phase between the input and the output so that the output phase lag is some safe amount less than 180 degrees (usually 45 degrees) at the frequency that the gain of the closed loop system is unity.
The gain vs frequency response curve of a typical prior art actuator servo loop is shown in FIG. 2(a). There, the vertical axis represents gain in decibels ("db"). The horizontal axis represents frequency. Curve 16 represents a typical frequency response. As shown, it starts out high and gradually drops. It crosses the zero db line typically around 400 hz. FIG. 2(b) shows the phase relationship of the output to that of the input of a prior art servo whose gain vs frequency response is shown as curve 16 in FIG. 2(a). In FIG. 2(b), the vertical axis represents phase lag between the output and the input and the horizontal axis represents frequency. Curve 18 is the phase vs frequency curve corresponding to the gain vs frequency curve 16 of FIG. 2(a). As can be seen from curve 18, the phase lag starts off at -270 degrees. This is because, this application requires 3 integrators and each integrator adds 90 degrees of phase lag at dc (zero hz). The compensation added to the feedback loop "peaks the phase" from -270 degrees to a safe -135 degrees by the time the gain curve reaches the zero db frequency. As mentioned previously, increasing disk drive performance demands are forcing designers to attempt to increase the open loop gain. All prior approaches at increasing the open loop gain have been centered on moving the entire gain vs frequency curve up as illustrated by dotted line 17 in FIG. 2(a). As can be seen, this approach does effectively increase the open loop gain at the disturbance frequency but it also increases the bandwidth. That is, the frequency at which the gain is unity has moved from 400 hz to 600 hz. But at 600 hz, the phase lag is back at -180 and the servo is unstable. Thus, in order to improve the open loop gain and keep the servo stable, the phase must be "peaked up" even more. This is expensive in that it requires higher performance components and more complex circuits, and there are practical limits as to how high the open loop gain can be pushed due to noise inherent in the system and the fact that the system is sampled.